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logician mathematician philosopher scientist
Ethnicity:
The Godels were part of the German-speaking minority in Brunn.
Godel was born in Brunn, Moravia (now Brno, Czech Republic), on April 28, 1906. He was the younger son of Rudolf Godel, who worked for a textile factory in Rrunn, and Marianne Handschuh. Godel had an older brother, Rudolf, who would study medicine and become a radiologist.
Godel's family had no allegiance to the nationalist sentiments around them, and all of Godel’s educational experience was in German-speaking surroundings.
Godel began his education in September, 1912, when he was enrolled in a Lutheran school in Brunn. In the fall of 1916 he became a student in a gymnasium, where he remained until 1924. At that point he entered the University of Vienna in 1924, planning to major in physics. In 1926, influenced by one of his teachers in number theory, he changed to mathematics; he did, however, retain an interest in physics, which he expressed in a number of unpublished papers later in life. He also continued his studies in philosophy and was associated with the Vienna Circle, a gathering of philosophers of science that had great influence on the English-speaking philosophical community.
Godel received his doctorate in February of 1930 for his proof of what became known as the completeness theorem.
In 1931 Gödel published his incompleteness theorems in Über formal unentscheidbare Sätze der "Principia Mathematica" und verwandter Systeme (called in English "On Formally Undecidable Propositions of "Principia Mathematica" and Related Systems"). In the paper Godel introduced a new technique which enabled him to discuss arithmetic using arithmetic.
Godel’s method of proof enabled him to introduce the technique of self-reference into the very foundations of mathematics; he showed that there were statements which were indisputably true but could not be proved by axiomatization.
Of the schools of mathematical philosophy most active at the time Godel introduced his incompleteness theorem, at least two have not since enjoyed the same reputation. Logicism was the belief that all mathematics could be reduced to logic and thereby put on a firm foundation. Formalism claimed that certainty could be achieved for mathematics by establishing theorems about completeness. In the aftermath of Godel’s work, it was even suggested that his theorem showed that man was more than a machine, since a machine could only establish what was provable, whereas man could understand what was true, which went beyond what was provable. Many logicians would dispute this, but no philosophy of mathematics is imaginable which does not take account of Godel’s work on incompleteness.
Godel was never a popular or successful teacher. His reserved personality led him to lecture more to the blackboard than to his audience. Fortunately, he was invited to join the Institute for Advanced Study at Princeton, which had opened in the fall of 1933, where he could work without teaching responsibilities. He remained there until 1978. Despite the attractions of the working environment in Princeton, Godel continued to return to Austria, and it was there that he lectured on his first major results in the new field to which he had turned attention, the theory of sets.
Set theory had been established as a branch of mathematics in the last half of the nineteenth century, although its development had been hindered by the discovery of a few paradoxes. As a result, many who studied the field felt it was important to produce an axiomatization that would prevent paradoxes from arising. The axiomatization which most mathematicians wanted was one which would capture the intuitions they had about the way sets behaved without necessarily committing them to points about which there was disagreement.
In 1950 he became a Plenary Speaker of the ICM in Cambridge, Massachusetts.
His mathematical accomplishments guaranteed his philosophical speculations a hearing, even if they ran counter to the dominant currents of thought at the time.
But Godel moved away from mathematics in his later years, he contributed occasionally to the field.
In his later years Godel was assaulted by fascist students, and he rapidly applied for a visa to the United States. It was a sign of his stature in the profession that at a time when so many were seeking to escape from Europe, Godel’s request was promptly granted. He never returned to Europe after his hasty departure.
His scientific works included five volumes. The first two include Gödel's publications; the third includes unpublished manuscripts from Gödel's Nachlass, and the final two include correspondence.
One of his last mathematical articles, published twenty years before his death, dealt with the attempt to formalize the approach to mathematical philosophy known as intuitionism. Godel himself was not partial to that approach, but his work had wide influence among the intuitionists.
Godel was appointed an ordinary member of the Institute for Advanced Study in Princeton, where he would remain for the rest of his life.
Gödel made an immense impact upon scientific and philosophical thinking in the 20th century.
Gödel is best remembered for his two incompleteness theorems, published in 1931. While working on mathematical logic, he discovered that there were some inherent limitations in every formal axiomatic system containing basic arithmetic. Later these theorems were found to be as much important for mathematical logic as for the philosophy of mathematics.
Five volumes of Gödel's collected works have been published.
For his achievements as a scientist he received several awards. Gödel was awarded the first Albert Einstein Award in 1951 with Julian Schwinger, and was also awarded the National Medal of Science, in 1974.
The Gödel Prize, an annual prize for outstanding papers in the area of theoretical computer science, is named after him.
In addition, The Kurt Gödel Society, founded in 1987, was named in his honor.
The University of Vienna hosts the Kurt Gödel Research Center for Mathematical Logic.
The Association for Symbolic Logic has invited an annual Kurt Gödel lecturer each year since 1990, as well.
Gödel was a convinced theist, in the Christian tradition. He held the notion that God was personal.
In an unmailed answer to a questionnaire, Gödel described his religion as "baptized Lutheran (but not member of any religious congregation). My belief is theistic, not pantheistic, following Leibniz rather than Spinoza. "Describing religion(s) in general, Gödel said: "Religions are, for the most part, bad—but religion is not". According to his wife Adele, "Gödel, although he did not go to church, was religious and read the Bible in bed every Sunday morning", while of Islam, he said, "I like Islam: it is a consistent [or consequential] idea of religion and open-minded".
Godel was baptized a Lutheran and took religion more to heart than the rest of his family.
Quotations:
"I don't believe in empirical science. I only believe in a priori truth. "
"Either mathematics is too big for the human mind or the human mind is more than a machine. "
"All generalisations - perhaps except this one - are false. "
Godel was a member of National Academy of Sciences, American Academy of Arts and Sciences, American Philosophical Society, Association for Symbolic Logic, as well as an honorary member of London Mathematics Society.
Godel had suffered a nervous breakdown in 1934 which aggravated an early tendency to avoid society. Godel had a distrust of medicine that amounted in his later years to paranoia.
In 1927, Kurt Gödel met Adele Nimbursky (née Porkert) at a night club, where she was employed as a dancer. Although his family did not approve of the match, he married her on September 20, 1938, just before they left for the United States.
She was six years older to Kurt Gödel and a divorcee.
